# isFJumpingExponent -- Checks whether a given number is an F-jumping number

## Synopsis

• Usage:
isFJumpingExponent(t,f,Verbose=>V)
• Inputs:
• t,
• f, , an element of a -Gorenstein ring
• V,
• Optional inputs:
• AssumeDomain =>
• FrobeniusRootStrategy => , default value Substitution, an option passed to computations in the TestIdeals package
• MaxCartierIndex => an integer
• QGorensteinIndex => an integer
• Outputs:

## Description

Returns true if t is an F-jumping number of f, otherwise it returns false. This function only works if the ambient ring of R is -Gorenstein

If the ambient ring of f is a domain, the option AssumeDomain can be set to true in order to speed up the computation. Otherwise AssumeDomain should be set to false.

Let R be the ambient ring of f. If the Gorenstein index of R is known, one should set the option QGorensteinIndex to the Gorenstein index of R. Otherwise the function attempts find the Gorenstein index of R, assuming it is between 1 and MaxCartierIndex. By default, MaxCartierIndex is set to 10.

The option FrobeniusRootStrategy is passed to an internal call of frobeniusRoot. The two valid values of FrobeniusRootStrategy are Substitution and MonomialBasis.

 `i1 : R = ZZ/5[x,y];` `i2 : f = x^4 + y^3 + x^2*y^2;` ```i3 : isFJumpingExponent(7/12,f) o3 = true``` ```i4 : isFJumpingExponent(4/5,f) o4 = true``` ```i5 : isFJumpingExponent(5/6,f) o5 = false``` ```i6 : isFJumpingExponent(11/12,f) o6 = true```